\[ y'(x)=\frac {\frac {x^2}{2}+x^3 \sqrt {x^2-4 y(x)+2 x+1}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.593976 (sec), leaf count = 49
DSolve[Derivative[1][y][x] == (1/2 + x + x^2/2 + x^3*Sqrt[1 + 2*x + x^2 - 4*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{4} \left (x^2-\frac {1}{9} \left (-2 x^3+3 x^2-6 x-6 \log \left (\frac {1}{x+1}\right )+6 c_1\right ){}^2+2 x+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.411 (sec), leaf count = 38
dsolve(diff(y(x),x) = 1/2*(x^2+2*x+1+2*x^3*(x^2+2*x+1-4*y(x))^(1/2))/(1+x),y(x))
\[c_{1}-\frac {2 x^{3}}{3}+x^{2}-2 x +2 \ln \left (1+x \right )-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0\]